Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

Due to its light mass, of order Lambda(QCD), the strange quark can play a special role in chiral symmetry breaking (chiSB): differences in the pattern of chiSB in the limits N-f = 2 (m(u),m(d) --> 0, m(s) physical) and N-f = 3 (m(u),m(d),m(s) --> 0) may arise due to vacuum fluctuations of s (s) over bar pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p(4)) low-energy constants L-4 and L-6. In case of large fluctuations, we show that the customary treatment of SU(3) x SU(3) chiral expansions generates instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming non-perturbatively vacuum fluctuations of s s-bar pairs, in order to extract information about chiSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavor analysis of the low-energy pipi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m(s)/(m(u) + m(d)) greater than or equal to 14 at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of chiSB in the N-f = 3 chiral limit.